An ignition system for producing sequential spark ignition is known in which a sequential spark ignition is triggered at the firing time and, as a result of the repeated successive control of the output stage upon each switching off of the current of the ignition coil an ignition spark is triggered on the secondary side. In this known arrangement, the ignition spark does not burn out before the time that the primary current is switched on again, so that a certain residual energy is present in the ignition coil upon the switching on again of the primary current. The charging of an individual ignition customarily has the same duration as the charging of the remaining individual ignitions of this sequential sparking ignition. This may have the result, particularly when losses of energy occur, for instance, in the ignition wiring or due to shunts at the spark plug, that the charging of an individual ignition is not sufficient to give off an ignition spark.